According to a survey, only 15% of customers who visited the website of a major retail store made a purchase. Random samples of size 50 are selected (show your workings clearly.

a) What is the sampling distribution of the sample proportion of customers who visited the website? State your reasons and identify the mean and the standard error.

b) What proportion of the samples will have between 20% and 25% of customers who will make a purchase after visiting the website?

c) 90% of the samples will have less than what percentage of customers who will make a purchase after visiting the website?

d) Construct a 95% confidence interval for the proportion of customers who visited the website.